TSTP Solution File: SYN270-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN270-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:33:51 EDT 2023
% Result : Unsatisfiable 97.58s 13.24s
% Output : Proof 97.58s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN270-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 20:13:27 EDT 2023
% 0.15/0.35 % CPUTime :
% 97.58/13.24 Command-line arguments: --no-flatten-goal
% 97.58/13.24
% 97.58/13.24 % SZS status Unsatisfiable
% 97.58/13.24
% 97.58/13.26 % SZS output start Proof
% 97.58/13.26 Take the following subset of the input axioms:
% 97.58/13.26 fof(axiom_12, axiom, ![X]: m0(a, X, a)).
% 97.58/13.26 fof(axiom_14, axiom, ![X2]: p0(b, X2)).
% 97.58/13.26 fof(axiom_18, axiom, p0(c, b)).
% 97.58/13.26 fof(axiom_20, axiom, l0(a)).
% 97.58/13.26 fof(axiom_5, axiom, s0(b)).
% 97.58/13.26 fof(axiom_9, axiom, r0(b)).
% 97.58/13.26 fof(prove_this, negated_conjecture, ~p4(b, b, c)).
% 97.58/13.26 fof(rule_029, axiom, ![I, H]: (m1(H, I, H) | (~p0(H, I) | ~s0(H)))).
% 97.58/13.26 fof(rule_050, axiom, ![D, E]: (n1(D, E, D) | (~s0(b) | (~l0(D) | ~p0(b, E))))).
% 97.58/13.26 fof(rule_062, axiom, ![F, D2, E2]: (n1(D2, D2, D2) | (~m0(E2, E2, F) | ~n1(E2, D2, E2)))).
% 97.58/13.26 fof(rule_152, axiom, ![C, D2, E2]: (p2(C, D2, D2) | (~n1(E2, D2, E2) | (~p0(C, D2) | ~p2(C, D2, C))))).
% 97.58/13.26 fof(rule_176, axiom, ![D2, E2]: (p2(D2, E2, D2) | ~m1(E2, D2, E2))).
% 97.58/13.26 fof(rule_267, axiom, ![B, C2, D2]: (r3(B, C2, B) | ~p2(B, D2, C2))).
% 97.58/13.26 fof(rule_285, axiom, ![G, H2]: (p4(G, G, H2) | (~r0(G) | ~r3(H2, G, H2)))).
% 97.58/13.26
% 97.58/13.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 97.58/13.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 97.58/13.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 97.58/13.26 fresh(y, y, x1...xn) = u
% 97.58/13.26 C => fresh(s, t, x1...xn) = v
% 97.58/13.26 where fresh is a fresh function symbol and x1..xn are the free
% 97.58/13.26 variables of u and v.
% 97.58/13.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 97.58/13.26 input problem has no model of domain size 1).
% 97.58/13.26
% 97.58/13.26 The encoding turns the above axioms into the following unit equations and goals:
% 97.58/13.26
% 97.58/13.26 Axiom 1 (axiom_20): l0(a) = true.
% 97.58/13.26 Axiom 2 (axiom_5): s0(b) = true.
% 97.58/13.26 Axiom 3 (axiom_9): r0(b) = true.
% 97.58/13.26 Axiom 4 (axiom_18): p0(c, b) = true.
% 97.58/13.26 Axiom 5 (axiom_14): p0(b, X) = true.
% 97.58/13.26 Axiom 6 (rule_062): fresh358(X, X, Y) = true.
% 97.58/13.26 Axiom 7 (axiom_12): m0(a, X, a) = true.
% 97.58/13.26 Axiom 8 (rule_050): fresh645(X, X, Y, Z) = true.
% 97.58/13.26 Axiom 9 (rule_152): fresh565(X, X, Y, Z) = true.
% 97.58/13.26 Axiom 10 (rule_029): fresh404(X, X, Y, Z) = m1(Y, Z, Y).
% 97.58/13.26 Axiom 11 (rule_029): fresh403(X, X, Y, Z) = true.
% 97.58/13.26 Axiom 12 (rule_050): fresh375(X, X, Y, Z) = n1(Y, Z, Y).
% 97.58/13.26 Axiom 13 (rule_152): fresh243(X, X, Y, Z) = p2(Y, Z, Z).
% 97.58/13.26 Axiom 14 (rule_176): fresh208(X, X, Y, Z) = true.
% 97.58/13.26 Axiom 15 (rule_267): fresh88(X, X, Y, Z) = true.
% 97.58/13.26 Axiom 16 (rule_285): fresh66(X, X, Y, Z) = p4(Y, Y, Z).
% 97.58/13.26 Axiom 17 (rule_285): fresh65(X, X, Y, Z) = true.
% 97.58/13.26 Axiom 18 (rule_050): fresh644(X, X, Y, Z) = fresh645(s0(b), true, Y, Z).
% 97.58/13.26 Axiom 19 (rule_062): fresh359(X, X, Y, Z, W) = n1(Y, Y, Y).
% 97.58/13.26 Axiom 20 (rule_152): fresh564(X, X, Y, Z, W) = fresh565(p0(Y, Z), true, Y, Z).
% 97.58/13.26 Axiom 21 (rule_029): fresh404(p0(X, Y), true, X, Y) = fresh403(s0(X), true, X, Y).
% 97.58/13.26 Axiom 22 (rule_050): fresh644(l0(X), true, X, Y) = fresh375(p0(b, Y), true, X, Y).
% 97.58/13.26 Axiom 23 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 97.58/13.26 Axiom 24 (rule_267): fresh88(p2(X, Y, Z), true, X, Z) = r3(X, Z, X).
% 97.58/13.26 Axiom 25 (rule_285): fresh66(r3(X, Y, X), true, Y, X) = fresh65(r0(Y), true, Y, X).
% 97.58/13.26 Axiom 26 (rule_152): fresh564(p2(X, Y, X), true, X, Y, Z) = fresh243(n1(Z, Y, Z), true, X, Y).
% 97.58/13.26 Axiom 27 (rule_062): fresh359(n1(X, Y, X), true, Y, X, Z) = fresh358(m0(X, X, Z), true, Y).
% 97.58/13.26
% 97.58/13.26 Goal 1 (prove_this): p4(b, b, c) = true.
% 97.58/13.26 Proof:
% 97.58/13.26 p4(b, b, c)
% 97.58/13.26 = { by axiom 16 (rule_285) R->L }
% 97.58/13.26 fresh66(true, true, b, c)
% 97.58/13.26 = { by axiom 15 (rule_267) R->L }
% 97.58/13.26 fresh66(fresh88(true, true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 9 (rule_152) R->L }
% 97.58/13.26 fresh66(fresh88(fresh565(true, true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 4 (axiom_18) R->L }
% 97.58/13.26 fresh66(fresh88(fresh565(p0(c, b), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 20 (rule_152) R->L }
% 97.58/13.26 fresh66(fresh88(fresh564(true, true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 14 (rule_176) R->L }
% 97.58/13.26 fresh66(fresh88(fresh564(fresh208(true, true, c, b), true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 11 (rule_029) R->L }
% 97.58/13.26 fresh66(fresh88(fresh564(fresh208(fresh403(true, true, b, c), true, c, b), true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 2 (axiom_5) R->L }
% 97.58/13.26 fresh66(fresh88(fresh564(fresh208(fresh403(s0(b), true, b, c), true, c, b), true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 21 (rule_029) R->L }
% 97.58/13.26 fresh66(fresh88(fresh564(fresh208(fresh404(p0(b, c), true, b, c), true, c, b), true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 5 (axiom_14) }
% 97.58/13.26 fresh66(fresh88(fresh564(fresh208(fresh404(true, true, b, c), true, c, b), true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 10 (rule_029) }
% 97.58/13.26 fresh66(fresh88(fresh564(fresh208(m1(b, c, b), true, c, b), true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 23 (rule_176) }
% 97.58/13.26 fresh66(fresh88(fresh564(p2(c, b, c), true, c, b, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 26 (rule_152) }
% 97.58/13.26 fresh66(fresh88(fresh243(n1(b, b, b), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 19 (rule_062) R->L }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(true, true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 8 (rule_050) R->L }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(fresh645(true, true, a, b), true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 2 (axiom_5) R->L }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(fresh645(s0(b), true, a, b), true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 18 (rule_050) R->L }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(fresh644(true, true, a, b), true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 1 (axiom_20) R->L }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(fresh644(l0(a), true, a, b), true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 22 (rule_050) }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(fresh375(p0(b, b), true, a, b), true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 5 (axiom_14) }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(fresh375(true, true, a, b), true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 12 (rule_050) }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh359(n1(a, b, a), true, b, a, a), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 27 (rule_062) }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh358(m0(a, a, a), true, b), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 7 (axiom_12) }
% 97.58/13.26 fresh66(fresh88(fresh243(fresh358(true, true, b), true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 6 (rule_062) }
% 97.58/13.26 fresh66(fresh88(fresh243(true, true, c, b), true, c, b), true, b, c)
% 97.58/13.26 = { by axiom 13 (rule_152) }
% 97.58/13.27 fresh66(fresh88(p2(c, b, b), true, c, b), true, b, c)
% 97.58/13.27 = { by axiom 24 (rule_267) }
% 97.58/13.27 fresh66(r3(c, b, c), true, b, c)
% 97.58/13.27 = { by axiom 25 (rule_285) }
% 97.58/13.27 fresh65(r0(b), true, b, c)
% 97.58/13.27 = { by axiom 3 (axiom_9) }
% 97.58/13.27 fresh65(true, true, b, c)
% 97.58/13.27 = { by axiom 17 (rule_285) }
% 97.58/13.27 true
% 97.58/13.27 % SZS output end Proof
% 97.58/13.27
% 97.58/13.27 RESULT: Unsatisfiable (the axioms are contradictory).
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